Domanda del libro di testo
State the name of the property illustrated: 3+17 = 17+3
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 1, Problema 13
Evaluate each exponential expression in Exercises 1–22.
Guida verificata passo dopo passo1
Identify the properties of exponents that apply to the expression \(2^2 \cdot 2^3\). Since the bases are the same (both are 2), you can use the product of powers property.
Recall the product of powers property: \(a^m \cdot a^n = a^{m+n}\). This means you add the exponents when multiplying with the same base.
Apply the property to the given expression: \(2^2 \cdot 2^3 = 2^{2+3}\).
Simplify the exponent by adding: \(2^{2+3} = 2^5\).
Express the final exponential form as \$2^5$, which is the simplified form of the original expression.
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Properties of Exponents
This concept involves the rules that govern how to manipulate expressions with exponents. For example, when multiplying powers with the same base, you add the exponents: a^m * a^n = a^(m+n). Understanding these properties is essential for simplifying exponential expressions.
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04:06
Rational Exponents
Base and Exponent
An exponential expression consists of a base and an exponent, where the base is the number being multiplied, and the exponent indicates how many times the base is used as a factor. For example, in 2^3, 2 is the base and 3 is the exponent, meaning 2 multiplied by itself three times.
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7:39Introduction to Exponent Rules
Evaluating Exponential Expressions
Evaluating an exponential expression means calculating its numerical value by performing the repeated multiplication indicated by the exponent. For instance, 2^3 equals 2 × 2 × 2 = 8. This step is necessary to find the final value of expressions like 2^2 * 2^3.
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03:11Evaluating Algebraic Expressions
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